DENVER, Colorado (CNN) -- The United States should scrap a significant portion of its nuclear arsenal, Sen. John McCain said Tuesday in a speech laying out his nuclear security policy.

McCain also spoke about canceling the development of nuclear "bunker-busting" bombs and working with Russia and China to prevent the spread of nuclear weapons.

"Today, we deploy thousands of nuclear warheads. It is my hope to move as rapidly as possible to a significantly smaller force," the presumptive Republican presidential nominee said at the University of Denver.

McCain advisers described the senator's policy as "significantly different" from that of President Bush in its goals and approach.

Protesters interrupted McCain's speech four times. The hecklers were escorted out of the room and shouted down by others in the audience chanting the candidate's name.

McCain linked his vision to that of President Reagan, an icon to conservatives, many of whom have been suspicious of the senator.

"A quarter of a century ago, President Ronald Reagan declared, 'Our dream is to see the day when nuclear weapons will be banished from the face of the Earth.' That is my dream, too," McCain said, adding that it was "a distant and difficult goal."

Reacting to the speech, a spokesman for Sen. Barack Obama, the Democratic front-runner, said that the substance of it mirrored Obama's positions but that McCain has no track record of leading on the issue.

"No speech by John McCain can change the fact that he has not led on nonproliferation issues when he had the chance in the Senate and that his support for a war against Iraq -- which had no active nuclear program -- diverted us from our efforts to secure loose nuclear materials, hampered our ability to pressure countries like North Korea and Iran, and set back our ability to lead the world against the threat of nuclear weapons," Obama spokesman Bill Burton said in a statement.

McCain took what appeared to be a veiled jab at Obama on Tuesday.

"Today, some people seem to think they've discovered a brand new cause, something no one before them ever thought of," he said.

"Many believe all we need to do to end the nuclear programs of hostile governments is have our president talk with leaders in Pyongyang and Tehran, as if we haven't tried talking to these governments repeatedly over the past two decades."

The two candidates have been trading attacks over Obama's stated willingness to talk to countries such as Iran.

Nevertheless, the message in McCain's speech was multilateral.

"The United States cannot and will not stop the spread of nuclear weapons by unilateral action," he said. "As powerful as we are, America's ability to defend ourselves and our allies against the threat of nuclear attack depends on our ability to encourage effective international cooperation." Watch more of McCain's speech »

The GOP candidate voiced support for the U.N. Security Council and International Atomic Energy Agency as well as an updated Nuclear Non-Proliferation Treaty.

"We also need to reverse the burden of proof when it comes to discovering whether a nation is cheating on its NPT commitments. The IAEA shouldn't have to play cat-and-mouse games to prove a country is in compliance," he said. Watch a report on McCain's vision for nuclear security »

It was noticeably more conciliatory toward Russia than the one in March, when McCain proposed ejecting the country from the Group of Eight nations. McCain also did not mention the United Nations in his March speech.

McCain gave qualified support to an international treaty banning the testing of nuclear weapons, the Comprehensive Nuclear Test Ban Treaty, which he opposed in the Senate in 1999.

And he proposed an "international repository for spent nuclear fuel" to keep the raw ingredients for nuclear bombs from falling into the wrong hands.

"It is even possible that such an international center could make it unnecessary to open the proposed spent nuclear fuel storage facility at Yucca Mountain in Nevada," McCain said, referring to a controversial project in the Southwest.

Randy Scheunemann, a senior foreign policy and national security advisor to the McCain campaign, said later that the repository could be in Siberia and that if there were sufficient security guarantees, McCain had a "willingness to entertain possibility ... that we could possibly send some of our spent fuel there."